Saturday, February 2, 2013

Analysis of the MegaMIllions lottery

I compiled some data in Excel using the winning numbers data
from 5-17-2002 – 3-23-2012.A few of the charts created using the winning
numbers for the Mega Millions
lottery are found below.

This first chart describes the number of times each number
is drawn for each pick. From the data we see that the number 2 is more likely
to be the first number drawn because it shows up as the first pick more often.
The number of times 2 has appeared first is 75.4% of the total number of times
a 2 has been in the winning numbers.

How many times each numbers is drawn

first pick

second pick

third pick

fourth pick

fifth pick

mega ball

1s

82

0

0

0

0

19

2's

92

9

0

0

0

21

3s

78

7

1

0

0

27

4's

70

23

1

0

0

24

5's

68

22

3

1

0

18

6's

61

21

3

0

0

22

7's

63

24

6

1

0

28

8's

53

27

4

0

0

22

9's

52

36

6

0

0

27

10's

50

46

13

0

0

27

11's

39

32

10

3

0

17

12's

35

44

16

2

0

21

13's

27

49

15

2

0

27

14's

46

40

19

2

1

16

15's

24

39

19

4

0

23

16's

32

42

16

10

0

15

17's

17

50

30

3

0

17

18's

23

40

27

10

1

21

19's

12

38

30

11

0

22

20's

13

40

38

7

1

24

21's

10

33

35

13

2

30

22's

14

34

32

13

4

25

23's

9

27

30

12

2

18

24's

14

32

36

10

3

23

25's

10

33

29

19

4

20

26's

5

25

39

19

2

22

27's

9

25

42

16

7

20

28's

5

20

35

34

5

9

29's

4

26

33

30

7

25

30's

2

23

27

29

8

21

31's

2

25

40

29

12

21

32's

1

19

34

35

10

15

33's

1

11

25

29

13

23

34's

0

8

31

29

11

26

35's

1

12

30

29

16

28

36's

1

10

25

41

21

32

37's

1

5

33

37

7

17

38's

1

6

25

40

22

25

39's

1

7

30

46

23

18

40's

0

5

19

45

23

20

41's

0

3

20

28

26

19

42's

0

3

18

43

29

23

43's

0

4

22

27

31

20

44's

0

1

18

32

42

21

45's

0

1

19

38

37

19

46's

0

1

11

44

47

17

47's

0

0

7

35

40

7

48's

0

0

12

41

55

4

49's

0

0

3

33

54

7

50's

0

0

2

25

74

4

51's

0

0

4

26

81

1

52's

0

0

2

17

89

10

53's

0

0

2

16

56

0

54's

0

0

1

8

50

0

55's

0

0

0

4

49

0

56's

0

0

0

0

63

0

In this next chart I have laid out the average, mode,
median, harmonic mean and other analysis of the number distributions across all
of the different picks.

first pick

second pick

third pick

fourth pick

fifth pick

mega ball

median all

7.5

18

28

38

49

24

Average all

9.278210117

18.6624514

28.3015564

37.42607

46.4542802

23.990272

mode all

2

17

27

39

52

36

standard deviation

7.137233978

9.10326996

10.2470703

9.59011029

7.6711884

13.842004

Geometric mean

6.565968069

16.139646

26.1471469

35.9559721

45.6978254

18.277583

Harmonic mean

4.207752217

13.1495089

23.5028125

34.0860285

44.7726832

10.698143

Mean - stddev

2.140976139

9.5591814

18.0544862

27.8359598

38.7830918

10.148268

Mean + stddev

14.63723398

27.10327

38.2470703

47.5901103

56.6711884

37.842004

avg mean+-stddev

8.389105058

18.3312257

28.1507782

37.713035

47.7271401

23.995136

This final chart is all of the data above rounded to the
nearest whole number.

first pick

second pick

third pick

fourth pick

fifth pick

mega ball

8

18

28

38

49

24

9

19

28

37

46

24

2

17

27

39

52

36

7

9

10

10

8

14

7

16

26

36

46

18

4

13

24

34

45

11

2

10

18

28

39

10

15

27

38

48

57

38

8

18

28

38

48

24

It is important to note, that all these numbers represent
the various distribution statistics of the numbers that were drawn at each of
the televised drawings, and do not represent any
regressive or other types of predictive models. These numbers are just simply a
statistical analysis of the given data for educational purposes only. All data
represents the real numbers published at http://www.megamillions.com/numbers/pastdrawings.asp
The website offers a tool at the top of the page to select your data range and
get all of the drawings